Pat chicken breasts dry with a paper towel. Drizzle 1 tablespoon of the olive oil over the chicken breasts. Season both breasts with the salt and pepper. Sprinkle with Herbes De Provence and press into the flesh of the chicken. Set aside.
Heat a 10" skillet over medium high heat. Add remaining two tablespoons of olive oil. When oil is hot, but not smoking add the chicken breasts, skin side down. Cook for 3-4 minutes without touching or agitating the chicken. Use a pair of tongs to flip the chicken and continue to cook for an additional 2 minutes. Transfer the chicken to a plate.
Add the onions and potatoes and cook for 3-4 minutes or until onions are slightly softened and start to take on some color. Turn the potatoes, cut side down onto the pan. Add slices of lemon and arrange so the lemon is in contact with the pan's surface.
Place the chicken breasts on top of the vegetables, skin side up and transfer to the hot oven. Roast the chicken for 15-20 minutes or until juices run clear.
Transfer chicken and vegetables to a serving platter and tent with aluminum foil.
Place the pan back on the stovetop over medium high heat (use an oven mitt - (the handle will be 425°). Add the butter and dijon to the pan and whisk to combine. Add the white wine and cook down until reduced by half. Add the chicken broth and simmer until reduced by half.
Drizzle sauce over the chicken and vegetables. Sprinkle with parsley to serve.